Recently, as an independent power plant with capacity of from several tens to several hundreds kilowatts, a gas turbine power generator has been studied which employs a gas turbine to operate a generator and which includes a regenerative heat exchanger. In such a gas turbine power generator, the number of rotations N and a fuel flow rate MF are adjusted to hold the number of rotations N at a minimum in the range satisfying a demanded load while referring to a turbine outlet temperature TOT and a regenerative heat exchanger outlet temperature TRO, thereby holding the combustion temperature as high as possible and increasing the efficiency of power generation.